Who were the War Lords?

Despite what some or the expanded universe stuff claims, I don't believe they were called the "war lords". There leader was called the War Lord. I believe they were one of the many warlike races in the Doctor Who universe. They were sensitive to bright light, but they were nothing particularly special. I assume they only knew about the Time Lords because of the War Chief.

The story made it pretty clear that the War Chief was the only Time Lord working with them.

They could have been amnesiac. 

Just a bunch of humanoids. The only odd thing is we don't hear their species name. Otherwise they're no more distinctive than the Dulcians. Or the Gonds.

I dunno, they were enough of a threat that the Doctor had to bite the proverbial bullet and sacrifice his freedom by summoning his people. Considering how he took care of the Daleks in what was supposed to be their final end, I'd say that they're a great deal more than just another group of hominids. Setting up the War Games must have taken a great deal of time, effort and specialised coordination, it was only their petty in-fighting which ultimately brought them down.

The Doctor had already defeated the aliens by the time he called the Timr Lords. What he really needed them for was returning all the soldiers home. He couldn't control the TARDIS back then, and the SIDRATs were all broken, so he had no other way to get everyone back to their own times.

True, and there were no guarantees that the aliens weren't going to send reinforcements once they'd found out what had happened with their latest operation. Remember that there was an entire homeworld that needed taking care of which could have rendered all the Doctor's efforts for naught.

Mmm, I suspect it wasn't quite as literal as just taking the best fighters and putting them onto the battlefield to be slaughtered.

I suspect the whole thing was a lot more anthropological, studying the various tactics and manoeuvres of the most efficient fighting force and implementing them into their own forces while simultaneously bolstering the physical hardiness of the remaining troops. The mental conditioning machine would've proved integral to them conforming and those who were unable to survive the process of augmentation -- whether mental so they charge forward irrespective of pain or physical where they have literal armour -- would simply be used as cannon fodder.

For instance, fighting the Cybermen you could have men like Carstairs injected with horrible techno-organic viruses like we saw in Second Chances that would erode the conversion unit and the victim themselves from the inside out. Then the remaining War Lords could have turned up and massacred the crippled survivors. They certainly have the technology on hand to manufacture and achieve such a scheme.

With the War Chief dead, and the SIDRATS not working, the aliens wouldn't have been able to go kidnap more soldiers. The Doctor was hoping that he would be able to send everyone home, and leave the aliens' plans thwarted. If the Doctor hadn't been forced to involve the Time Lords, the aliens probably would have popped up again at some point, with some other insane scheme, and the Doctor would have just stopped them again and again like he does with most of his enemies.

The Doctor would have left their planet before they had a chance to do anything to him. And if they did take Jamie and Zoe hostage, he would have outwitted them somehow, because that is what he always does. The Doctor's usual method is to defeat the bad guys, but leave the species alive to show up in another episode. That's why the Daleks, Cybermen, Sontarans, Ice Warriors, Weeping Angels, Nestene, Silurians, and all the other ones are able to make repeat appearances. The only reason that the Doctor was so desperate that he had to call the Time Lords was because he couldn't get all of the soldiers home, not because the aliens were too great a threat for him to deal with.